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Permutation and Combination - Quant/Math - CAT 2013
Question 4 the day:
May 20, 2003
The question for the day is from the topic of Permutation and Combination.
- A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
| (1) |
9 |
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(2) |
26 |
| (3) |
126 |
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(4) |
3920 |
Correct Answer - (3)
Solution:
There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Or Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in 8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4 ways.
Therefore, the total number of ways in which 8 students can travel is 8C3 + 8C4 = 56 + 70 = 126.
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